Random Jason Timeout Test 012

Average Error: 61.3 → 60.4

Time: 28.9s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.023379392650477e+110

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

\[\log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]

C

double f(double a) {
        double r3098 = a;
        double r3099 = cosh(r3098);
        double r3100 = r3098 * r3098;
        double r3101 = fmod(r3099, r3100);
        double r3102 = log1p(r3098);
        double r3103 = pow(r3101, r3102);
        double r3104 = acos(r3103);
        return r3104;
}

↓

double f(double a) {
        double r3105 = a;
        double r3106 = cosh(r3105);
        double r3107 = r3105 * r3105;
        double r3108 = fmod(r3106, r3107);
        double r3109 = exp(r3108);
        double r3110 = log(r3109);
        double r3111 = log1p(r3105);
        double r3112 = pow(r3110, r3111);
        double r3113 = acos(r3112);
        double r3114 = exp(r3113);
        double r3115 = sqrt(r3114);
        double r3116 = log(r3115);
        double r3117 = r3116 + r3116;
        return r3117;
}

Error

Bits error versus a

Derivation

1. Initial program 61.3

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
2. Using strategy rm

3. Applied add-log-exp 60.4

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
4. Using strategy rm

5. Applied add-log-exp 60.4

   \[\leadsto \color{blue}{\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}\]
6. Using strategy rm

7. Applied add-sqr-sqrt 60.4

   \[\leadsto \log \color{blue}{\left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}} \cdot \sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)}\]

8. Applied log-prod 60.4

   \[\leadsto \color{blue}{\log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)}\]

9. Final simplification 60.4

   \[\leadsto \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))